Ionizational Nonequilibrium and Ignition in Plasma Accelerators

The focus of this work is on identifying the processes behind the sustained initiation of ionization, or "ignition", at the inlet of a self-field magnetoplasmadynamic thruster (MPDT). Plasma accelerators generate high Isp thrust via a combination of high power densities and low mass densities, resulting in strong gradients of temperature and density, particularly in the areas of current concentration. Thermodynamic equilibrium is generally a poor assumption under such high power loading and this effects the excited state population distribution which is needed for calculating the overall recombination coefficients used in numerical flow models. These nonequilibrium conditions must be understood in order to accurately model the plasma. A classical approach is adapted to characterize the nonequilibrium ionization problem. Atomic or ionic species are modeled by their electronically excited state structure for detailed finite-rate analysis of multi-step ionization processes, including both inelastic collisions and radiation (in a parametric form). The time scales for the excited states are found to be small enough compared to the ground state's to make the quasi-steady-state-solution assumption, which allows the excited state population distribution relative to the ground state to be determined by a modified mass balance law. Neglecting radiative effects, which are shown to be small in MPDTs, the overall rate coefficients for electron-neutral ionization collisions and electron-electron-ion recombination collisions are calculated for the hydrogen atom, and the argon atom and first ion. These rate models are applied to the problem of ignition in a self-field MPDT, where the propellant is injected into the thruster neutral, but the plasma must be at least partially ionized at the inlet for effective electromagnetic thrust. Backdiffusion is assumed to be responsible for transporting electron-ion pairs back to the inlet wall (which is ion-attracting), and sustaining the initiation of ionization there. This approach is similar to that taken in diffusion flames, and other diffusion-reaction situations. Results from a simple, but illustrative, constant speed igntion model indicate that there is a "blowoff speed" ignition criterion. That is, if the propellant is injected at a speed less than the blowoff speed, then back-diffusion is sufficient to supply the inlet wall with enough electrons to initiate ionization. If the propellant is injected at a speed greater than the blowoff speed, then diffusion cannot supply the inlet with electrons, and the ionization front gets "blown" downstream. This explanation should hold generally even for the more realistic accelerating flow case. For atomic injection, the blowoff speed depends on the ambipolar coefficient, and the ionization rate constant of the propellant. Therefore, propellants of high diffusivity and low ionization potential will ignite more readily at a given temperature. Although temperature variation in the ionizing region is found to have little effect on the ignition of a constant speed plasma, the ionization rate coefficient is a strong function of the electron temperature, which is set by an overall energy balance in the channel. In the accelerating plasma ignition model, both momentum and energy are accounted for self-consistently. The resulting inlet speeds were generally small enough to avoid "blowoff", and the ionizing length scales were on the order of mm and were shorter than the magnetic diffusion scale length under typical self-field MPDT conditions. It was found that increasing the contraction ratio in the thruster channel lowered the electron temperature, which tended to quench ionization and stretch out the ionizing region. This work has shown that the initiation of ionization at the inlet of an MPDT may be explained by convective, diffusive, and collisional ionization processes alone, and is the first step towards a complete understanding of the initial ionization process in self-field MPDTs. Thesis Supervisor: Professor Manuel Martinez-Sanchez Department of Aeronautics and Astronautics